Observation and description of changes in the world around us
are the first steps in finding and learning about patterns.
The Essential Question of Investigation 3 is... How can I visually explain situations where one thing changes based on another? Notes from Class:
Profit is not equal to costs - income because subtraction is not commutative.
Profit = income - costs
Non-Commutative Mathematical
Operations
Commutative Mathematical
Operations
Subtraction: 10-7=3 is not equal to -3=7-10
Division: 3/5= 0.6 is not equal to 1 2/3 =5/3
Addition: 10+7= 17 = 17 =7+10
Multiplication: 20x4= 80 = 80 = 4x20
Problem 3.3: Predicting Profit
Based on the results of their survey, the tour operators decided to charge $350 per person for the tour. Of course, not all of this money would be profit. To estimate their profit, they had to consider the expenses involved in running the tour. Sidney estimated these expenses and calculated the expected profit for various numbers of customers. She made the graph below to present her predictions to her partners. Since the profit depends on the number of tour customers, she put the number of customers on the x-axis.
Problem 3.3 Study the graph above. A. How much profit will be made if 10 customers go on the tour? 25 customers? 40 customers?
There will be a $150 if 10 customers go on the tour. $380 profit if 25 customers go on the tour. There will be $600 profit if 40 people go on the tour.
B. How many customers are needed for the partners to earn a $200 profit? A $500 profit? A $600 profit?
There will have to be 14 customers to earn a $200 profit. There have to be 34 or 35 customers to earn a $500 profit. It would take the partners 41 customers to get a $600 profit.
C. How does the profit change as the number of customers increases? How is this pattern shown in the graph?
The graph grows steadily up as the number of customers go up. There is a $150 profit every 10 customers.
D. If the tour operators reduced their expenses but kept the price at $350, how would this change the graph?
If the partners reduced their expenses but kept the price of $350, the profit pattern will go up in a steady pace but will gradually slant and will become less steap.
Problem 3.3 Follow-Up In the profit graph, points at the intersection of two grid lines, such as (20, 300) and (40, 600), are easy to read. Use the “easy to read” points to figure out what the profit would be if only 1 customer went on the tour. How about 2 customers? 3 customers? 100 customers? Describe, in words, the estimated profit for any number of customers.
1 customer: $15
2 customers: $30
3 customers: $75
100 customers: $1500
It is easy to find the profit made by any number of customers. For a number of customers under 10, you can easily multiply $15 by any number to get the one-digit-number-of-customers. If the number of customers is in 10s, then we can multiply $150 by a number. A profit out of a number of customers in thousands could be made by multiplied $1500 by a number. So, in order to get a profit out of 154 customers, we will have do: $1500 + ($150 x 2) + ($15 x 4) = $1860
PROBLEM 3.3: PREDICTING PROFIT
The Big Idea is...
Observation and description of changes in the world around usare the first steps in finding and learning about patterns.
The Essential Question of Investigation 3 is... How can I visually explain situations where one thing changes based on another?
Notes from Class:
Profit is not equal to costs - income because subtraction is not commutative.
Profit = income - costs
Operations
Operations
Problem 3.3: Predicting Profit
Based on the results of their survey, the tour operators decided to charge $350 per person for the tour. Of course, not all of this money would be profit. To estimate their profit, they had to consider the expenses involved in running the tour. Sidney estimated these expenses and calculated the expected profit for various numbers of customers. She made the graph below to present her predictions to her partners. Since the profit depends on the number of tour customers, she put the number of customers on the x-axis.
Problem 3.3
Study the graph above. A. How much profit will be made if 10 customers go on the tour? 25 customers? 40 customers?
There will be a $150 if 10 customers go on the tour. $380 profit if 25 customers go on the tour. There will be $600 profit if 40 people go on the tour.
B. How many customers are needed for the partners to earn a $200 profit? A $500 profit? A $600 profit?
There will have to be 14 customers to earn a $200 profit. There have to be 34 or 35 customers to earn a $500 profit. It would take the partners 41 customers to get a $600 profit.
C. How does the profit change as the number of customers increases? How is this pattern shown in the graph?
The graph grows steadily up as the number of customers go up. There is a $150 profit every 10 customers.
D. If the tour operators reduced their expenses but kept the price at $350, how would this change the graph?
If the partners reduced their expenses but kept the price of $350, the profit pattern will go up in a steady pace but will gradually slant and will become less steap.
Problem 3.3 Follow-Up In the profit graph, points at the intersection of two grid lines, such as (20, 300) and (40, 600), are easy to read. Use the “easy to read” points to figure out what the profit would be if only 1 customer went on the tour. How about 2 customers? 3 customers? 100 customers? Describe, in words, the estimated profit for any number of customers.
- 2 customers: $30
- 3 customers: $75
- 100 customers: $1500
It is easy to find the profit made by any number of customers. For a number of customers under 10, you can easily multiply $15 by any number to get the one-digit-number-of-customers. If the number of customers is in 10s, then we can multiply $150 by a number. A profit out of a number of customers in thousands could be made by multiplied $1500 by a number. So, in order to get a profit out of 154 customers, we will have do:1 customer: $15
$1500 + ($150 x 2) + ($15 x 4) = $1860
USEFUL RESOURCES: